Any description of the emergence and evolution of different types of meaning processes (semiosis, sensu C.S.Peirce) in living systems must be supported by a theoretical framework which makes it possible to understand the nature and dynamics of such processes. Here we propose that the emergence of semiosis of different kinds can be understood as resulting from fundamental interactions in a triadically-organized hierarchical process. To grasp these interactions, we develop a model grounded on Stanley Salthe's hierarchical structuralism. This model can be (...) applied to establish, in a general sense, a set of theoretical constraints for explaining the instantiation of different kinds of meaning processes (iconic, indexical, symbolic) in semiotic systems. We use it to model a semiotic process in the immune system, namely, B-cell activation, in order to offer insights into the heuristic role it can play in the development of explanations for specific semiotic processes. (shrink)